Lecture Notes | Number Theory II: Class Field Theory | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Dr. Sam Raskin

Departments

Mathematics

As Taught In

Spring 2016

Level

Graduate

Topics

Mathematics

Algebra and Number Theory

Topology and Geometry

Learning Resource Types

Lecture Notes

Problem Sets

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Lecture Notes

Artin and Brauer Reciprocity, Part I

Artin and Brauer Reciprocity, Part II

Brauer Groups

Chain Complexes and Herbrand Quotients

Derived Functors and Explicit Projective Resolutions

Exact Sequences and Tate Cohomology

GCFT and Quadratic Reciprocity

Hilbert Symbols

Homotopy Coinvariants, Abelianization, and Tate Cohomology

Homotopy, Quasi-Isomorphism, and Coinvariants

Introduction

Lectures on Cohomological Class Field Theory

Non-Degeneracy of the Adèle Pairing and Exact Sequences

Norm Groups with Tame Ramification

Norm Groups, Kummer Theory, and Profinite Cohomology

Proof of the First Inequality

Proof of the Second Inequality

Proof of the Vanishing Theorem

Tate Cohomology and Inverse Limits

Tate Cohomology and K[superscript unr]

The Mapping Complex and Projective Resolutions

The Vanishing Theorem Implies Cohomological LCFT

Vanishing of Tate Cohomology Groups

Hilbert’s Theorem 90 and Cochain Complexes

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